Question: Rewrite as a simplified fraction. ${3.6\overline{5} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 365.5555...\\ 10x &= 36.5555...\end{align*}}$ Subtracting the two equations, we have: ${90x = 329}$ ${x = \dfrac{329}{90}} \text{or} {3 \dfrac{59}{90}}$